Treasurer Joe Hockey said in June that PPL legislation would be introduced ‘‘soon’’ and described as ‘‘absurd’’ suggestions the policy had been stalled due to internal unrest.

But a government source said the scheme had been placed in the “too-hard basket” because the Coalition was fighting on too many fronts and struggling to get its basic budget measures passed by the Senate.

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Several other sources said a message had been discreetly sent to Mr Abbott that his pet policy could face an embarrassing defeat in the Senate.

Coalition senator Ian Macdonald had been an outspoken critic of the policy and welcomed the delay.

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“I’m pleased that Mr Abbott has listened to the overwhelming majority of Australians in deferring the scheme until the country can afford it,” he said.

Nationals senator John Williams had previously said the scheme should only be introduced when the economy was performing strongly, when there was a “four” in front of economic growth and the unemployment rate.

“Affordability remains the issue and also the problems in the childcare industry need to be addressed,” he said.

Crossbench senators Bob Day and Nick Xenophon urged Mr Hockey to scrap the scheme during budget negotiations in Adelaide last week.

When challenged, Mr Abbott refused to back down on the scheme, saying he did not break his promises and his critics would be the first to attack him for going back on his word if he heeded their calls.

But Senator Day said the “world had changed” since Mr Abbott surprised his party room with the policy in 2010 and “the electorate would not see it as a broken promise”.

“What you never have, you never miss,” Senator Day said.

The Greens were the only crossbenchers supporting Mr Abbott’s scheme but said there had been no negotiations since earlier this year when they demanded the government spelt out the details of how the scheme would work and insisted it be funded entirely by business.

“We’re just waiting to see if it’s still a policy they want to pursue,” Greens MP Adam Bandt said.

Mr Abbott’s “signature policy” would award new mothers their full pay for six months, capped at $50,000, after the birth of their child. It would be partly funded by a 1.5 per cent levy on big companies.

One source said the idea was friendless within cabinet, the exception being Mr Abbott. Business also opposed the scheme. Last week outgoing NAB chief executive Cameron Clyne said it would cost the bank $100 million in extra taxes and would not improve workplace productivity. He also believed the money would be better spent on childcare.

If the paid parental leave bills establishing Mr Abbott’s scheme were passed early next year, it could be running in time for the planned start date of July 1.